Four Zeros of a Spliced Function

★ 7/10functions Quadratic Equations Absolute Value Casework

Problem

Let

f(x)=\begin{cases}x^3,&x\geqslant 0,\\ -x,&x<0,\end{cases}

and let $g(x)=f(x)-|kx^2-2x|$ , where $k\in\mathbb R$ . Suppose $g(x)$ has exactly $4$ zeros. Find the range of $k$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Quadratic Equations, Absolute Value, Casework

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